Relevant bibliographies by topics / Zernike

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Zernike'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Zernike"

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Theodoridis, Thomas, Kostas Loumponias, Nicholas Vretos, and Petros Daras. "Zernike Pooling: Generalizing Average Pooling Using Zernike Moments." IEEE Access 9 (2021): 121128–36. http://dx.doi.org/10.1109/access.2021.3108630.

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Singh, Chandan, Ekta Walia, and Neerja Mittal. "Discriminative Zernike and Pseudo Zernike Moments for Face Recognition." International Journal of Computer Vision and Image Processing 2, no. 2 (2012): 12–35. http://dx.doi.org/10.4018/ijcvip.2012040102.

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Usually magnitude coefficients of some selected orders of ZMs and PZMs have been used as invariant image features. The careful selection of the set of features, with higher discrimination competence, may increase the recognition performance. In this paper, the authors have used a statistical method to estimate the discrimination strength of all the extracted coefficients of ZMs and PZMs whereas for classification, only the coefficients with estimated higher discrimination strength are used in the feature vector. The performance of these selected Discriminative ZMs (DZMs) and Discriminative PZMs (DPZMs) features have been compared to that of their corresponding conventional approaches on YALE, ORL and FERET databases against illumination, expression, scale and pose variations. An extension to these DZMs and DPZMs have been proposed by combining them with PCA and FLD. It has been observed from the exhaustive experimentation that the recognition rate is improved by 2-6%, at reduced dimensions and with less computational complexity, than that of using the successive ZMs and PZMs features.
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Singh, Chandan, Neerja Mittal, and Ekta Walia. "Face recognition using Zernike and complex Zernike moment features." Pattern Recognition and Image Analysis 21, no. 1 (2011): 71–81. http://dx.doi.org/10.1134/s1054661811010044.

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Chong, Chee-Way, P. Raveendran, and R. Mukundan. "An Efficient Algorithm for Fast Computation of Pseudo-Zernike Moments." International Journal of Pattern Recognition and Artificial Intelligence 17, no. 06 (2003): 1011–23. http://dx.doi.org/10.1142/s0218001403002769.

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Pseudo-Zernike moments have better feature representation capability, and are more robust to image noise than those of the conventional Zernike moments. However, due to the computation complexity of pseudo-Zernike polynomials, pseudo-Zernike moments are yet to be extensively used as feature descriptors as compared to Zernike moments. In this paper, we propose two new algorithms, namely coefficient method and p-recursive method, to accelerate the computation of pseudo-Zernike moments. Coefficient method calculates polynomial coefficients recursively. It eliminates the need of using factorial functions. Individual order or index of pseudo-Zernike moments can be derived independently, which is useful if selected orders or indices of moments are needed as pattern features. p-recursive method uses a combination of lower order polynomials to derive higher order polynomials with the same index q. Fast computation is achieved because it eliminates the requirements of calculating polynomial coefficients, Bpqk, and power of radius, rk, in each polynomial. The performance of the proposed algorithms on moment computation and image reconstruction, as compared to those of the present methods, are experimentally verified using a set of binary and grayscale images.
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Haidar, Riad. "Frederik « Frits » Zernike." Photoniques, no. 73 (September 2014): 20–22. http://dx.doi.org/10.1051/photon/20147320.

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Al-Rawi, Mohammed. "Fast Zernike moments." Journal of Real-Time Image Processing 3, no. 1-2 (2008): 89–96. http://dx.doi.org/10.1007/s11554-007-0069-2.

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Rahbar, Kambiz, Karim Faez, and Ebrahim Attaran Kakhki. "Phase wavefront aberration modeling using Zernike and pseudo-Zernike polynomials." Journal of the Optical Society of America A 30, no. 10 (2013): 1988. http://dx.doi.org/10.1364/josaa.30.001988.

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Qin, Hua Feng, Lan Qin, and Jun Liu. "A Novel Recurrence Method for the Fast Computation of Zernike Moments." Applied Mechanics and Materials 121-126 (October 2011): 1868–72. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.1868.

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A new method is proposed for fast computation of Zernike moments. This method presents a recursive relation to compute the entire set of Zernike moments. The fast computation is achieved because it involves less addition and multiplication operations. The experimental results show that the proposed method for the fast computation of Zernike moments is much more efficient than existing fast methods in most cases
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Liu, Zhenghui, and Hongxia Wang. "A Speech Content Authentication Algorithm Based on Pseudo-Zernike Moments in DCT Domain." International Journal of Digital Crime and Forensics 5, no. 3 (2013): 15–34. http://dx.doi.org/10.4018/jdcf.2013070102.

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A speech content authentication algorithm based on pseudo-Zernike moments in DCT domain is proposed in this paper, which is aimed at some shortcomings in some existing digital watermark schemes. The definition of coefficients self-correlation degree is given. Then the frequency domain watermark embedding method based on pseudo-Zernike moments in DCT domain is proposed. Watermark bits are generated by coefficients self-correlation degree and embedded by quantizing the pseudo-Zernike moments of DCT domain low-frequency coefficients. Comparing with the existing audio watermark algorithms based on pseudo-Zernike moments, the algorithm increases the watermarking embedding capacity and improves the efficiency greatly. Theoretical analysis and experimental evaluation results show that the proposed speech content authentication algorithm is effective.
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Luo, Yong. "Analysis and Optimization of Image Quality Evaluation Function in Computer-aided Alignment of Precision Optical System." Modern Applied Science 14, no. 6 (2020): 29. http://dx.doi.org/10.5539/mas.v14n6p29.

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The consistent application of computer-aided alignment technology could surmount aimlessness and significantly shorten the align period of complex optical systems. Wherein, the appropriate system image evaluation function is the primary condition to solve the system misalignment successfully. This paper first establishes the relationship between the amount of misalignment and the system aberration through mathematical modelling and then analyzes the relationship between Zernike coefficient, geometric aberration and system image quality in detail, proposes to construct a system image evaluation system using the idea of Zernike coefficient weighting to solve the problem of numerical instability and imprecision of the solutions caused by the direct selection of Zernike coefficients. Subsequently, the experimental alignment of an infrared optical system was performed using the optical system image quality evaluation method established in this paper. The alignment results showed that the RMS value of the system image quality improved by 24.8% under the same solving algorithm compares to the direct selection of the Zernike coefficient and the weighted Zernike coefficient as the system image quality evaluation function. Therefore, the application of the weighted Zernike coefficient-based optical system image evaluation function proposed in this paper is reasonable, feasible, and effective in the computer-aided alignment process.
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Dissertations / Theses on the topic "Zernike"

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MALLART, RAOUL. "Le theoreme de van cittert zernike. Application a l'acoustique adaptative." Paris 11, 1991. http://www.theses.fr/1991PA112270.

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Cette these traite deux problemes de l'echographie: la reduction du speckle et la focalisation en milieu inhomogene. Elle utilise une approche nouvelle qui repose sur une investigation du champ de pression retrodiffuse par un milieu totalement incoherent. Le theoreme de van cittert zernike est generalise a l'acoustique. Ce theoreme relie la fonction de covariance spatiale du champ de pression retrodiffuse au diagramme d'insonification incident par une transformee de fourier. Cette relation permet de faire apparaitre des invariances propres au mode echographique: la covariance spatiale est egale a l'autocorrelation de l'ouverture d'emission. L'emploi de barrettes de transducteurs a permis de verifier experimentalement ce theoreme. Le theoreme de van cittert zernike permet de prevoir l'amelioration maximale du snr en traitement incoherent. La focalisation en milieu inhomogene est abordee pour des inhomogeneites confinees en champ proche de la sonde. On explique les resultats classiques: influence de la frequence, de la taille de l'ouverture, des statistiques spatiales des inhomogeneites et de la distance inhomogeneites/sonde. On introduit une mesure echographique, non-invasive de la focalisation. L'exploitation de cette mesure permet de comprendre le fonctionnement particulier de deux techniques d'acoustique adaptative. On souligne la particularite du fonctionnement en mode echographique de ces techniques et l'importance fondamentale de l'iteration du processus. Nous proposons enfin des strategies de refocalisation qui tiennent compte de l'aspect temps reel et l'echographie et soulignons les limitations de ces techniques
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Huang, Tao. "Differential Zernike filter for phasing of segmented mirror and image processing." Thesis, Heriot-Watt University, 2009. http://hdl.handle.net/10399/2221.

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The major objective of this thesis is to study the differential Zernike filter and its applications in phasing segmented mirror and image processing. In terms of phasing, we provide both theoretical analysis and simulation for a differential Zernike filter based phasing technique, and find that the differential Zernike filter perform consistently better than its counterpart, traditional Zernike filter. We also combine the differential Zernike filter with a feedback loop, to represent a gradient-flow optimization dynamic system. This system is shown to be capable of separating (static) misalignment errors of segmented mirrors from (dynamical) atmospheric turbulence, and therefore compress the effects of atmospheric turbulence. Except for segmented mirror phasing, we also apply the Zernike feedback system in image processing. For the same system dynamics as well as in segment phasing, the Zernike filter feedback system is capable of compress the static noisy background, and makes the single particle tracking algorithm even working in case of very low signal-to-noise ratio. Finally, we apply an efficient multiple-particle tracking algorithm on a living cell image sequence. This algorithm is shown to be able to deal with higher particle density, while the single particle tracking methods are not working under this condition.
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Manuel, Anastacia Marie. "Field-dependent aberrations for misaligned reflective optical systems." Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/193941.

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The performance of optical imaging systems relies on control of aberrations that can arise from limitations in the design, manufacture, or alignment. This dissertation addresses the form of aberrations that occur for misaligned reflective systems, such as telescopes. The relationship between a characteristic set of field-dependent aberrations and the misalignments that cause them is systematically explored. A comprehensive technique that quantifies field performance for a 5-mirror system is given, using Monte Carlo analysis to provide confidence levels of image quality as functions of manufacturing and alignment errors. This analysis is an example of the "forward problem"— determining optical performance of a system if the errors are assumed. The inverse problem — determining the state of alignment based on measurements of performance — is more difficult. The solution to the inverse problem for a multiple mirror system requires an understanding of the complex coupling between many degrees of freedom (tilt, decenter, despace, shape error) of the optical elements and field-dependent aberrations.This work builds on previous treatment of field dependent optical aberrations from Tessieres, Thompson, Shack, Buchroeder and others. A basis set of field-dependent aberrations orthogonal over both field and pupil are developed here and used to describe systems with misaligned and misshapen optics. This description allows complete representation of high order and non-linear effects. The functional form of aberrations that are characteristic of mirror tilt, shift, and deformation show some useful patterns that provide insight to the fundamental effects of misalignment.The use of singular value decomposition to create orthogonal combinations of the field dependent aberrations provides a powerful tool for evaluating a system and for estimating the state of alignment using wavefront measurements. The following optical systems are evaluated to investigate the linear coupling between misalignment and the resulting field dependent aberrations:* 2-mirror telescopes, evaluating well-understood effects for an axisymmetric system and developing the relationships for an unobscured system.* 4-mirror correctors for a spherical primary telescope.The tools and methods are applied to reflective optical systems for astronomical telescopes, but the methods are general and can be useful for any optical imaging system.
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Williams, Kaitlyn Elizabeth, and Kaitlyn Elizabeth Williams. "Parametrizing Freeform Optical Surfaces for the Optimized Design of Imaging and Illumination Systems." Thesis, The University of Arizona, 2017. http://hdl.handle.net/10150/624141.

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Two optical design scenarios—imaging and illumination—were investigated for their use of Cartesian- and polar-based functions to generate freeform optical surfaces. The imaging scenario investigated a single-element, refracting freeform surface that converts an on-axis object field to an off-axis image point. XY polynomials (Cartesian but not orthogonal) and Zernike polynomials (Polar and orthogonal) were the two different function sets used to manipulate the surfaces to achieve the freeform imaging scenarios. The investigation discovered that the results between both function sets did not differ enough to single out a more effective surface type. However, the results did indicate that the Zernike function set typically required fewer coefficients to converge on an optimal imaging solution. The illumination scenario utilized an architectural lighting situation surrounding the Rothko exhibit for Green on Blue at the University of Arizona Museum of Art. The source location was fixed to the light track in the exhibit space and pointed in many different orientations towards the painting. For each orientation, a point cloud of a freeform optical surface was generated such that the painting surface was illuminated with uniform and low-level light. For each of these generated point clouds, a Legendre (Cartesian and orthogonal) and a Zernike (polar and orthogonal) fitting function was applied, and the convergence results were compared. In general, it was found that, after the 20th included fit term, the Legendre function resulted in a smaller RMS fit error than the Zernike function. However, if the light source was pointed near the center of the painting, the Zernike function converged on a solution with fewer fit terms than Legendre. Amidst the imaging scenario, a definition for the extent to which a surface was freeform, or the "freeformity", was given. This definition proved to be an effective solution when the image size was compared for an F/3.33, F/4, F/5, and F/6.67 system for a range of different image focusing heights: the image size trends for each F-number overlapped, indicating a universal freeform term. In addition, a recursive formula for Cartesian Zernike polynomials was defined, which was used to generate an infinite number of Zernike terms using one single recursive expression.
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Tang, Yiping. "A study of fluid behavior by a general analytical solution of the Ornstein-Zernike equation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq26141.pdf.

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Khatchadourian, Sonia. "Mise en œuvre d'une architecture de reconnaissance de formes pourla détection de particules à partir d'images atmosphériques." Cergy-Pontoise, 2010. http://www.theses.fr/2010CERG0438.

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L'expérience HESS consiste en un système de télescopes permettant d'observer les rayonnements cosmiques. Compte tenu des résultats majeurs obtenus depuis son installation, la seconde phase du projet a été engagée. Celle-ci passe par l'ajout d'un télescope plus sensible et plus grand que ses prédécesseurs. Toutes les données collectées par ce télescope ne pouvant être conservées à cause des limites de stockage, un système de déclencheur (trigger) performant doit être mis en place. L'objectif de cette thèse est de proposer une solution de reconnaissance de formes en temps réel, embarquée sur le télescope. La première partie de la thèse a consisté à élaborer une chaine de reconnaissance des formes pour ce trigger. Une chaine de traitement à base de réseau de neurones et des moments de Zernike a été validée. La seconde partie de la thèse a porté sur l'implantation des algorithmes retenus sur FPGA en tenant compte des contraintes en termes de ressources et de temps d'exécution<br>The HESS experiment consists of a system of telescopes destined to observe cosmic rays. Since the project has achieved a high level of performances, a second phase of the project has been initiated. This implies the addition of a new telescope which is capable of collecting a huge amount of images. As all data collected by the telescope can not be retained because of storage limitations, a new real-time system trigger must be designed in order to select interesting events on the fly. The purpose of this thesis was to propose a trigger solution to efficiently discriminate events captured by the telescope. The first part of this thesis was to develop pattern recognition algorithms to be implemented within the trigger. A processing chain based on neural networks and Zernike moments has been validated. The second part of the thesis has focused on the implementation of the proposed algorithms onto FPGA, taking into account the application constraints in terms of resources and execution time
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Lewis, Nathan Dean. "Corneal Topography Measurements for Biometric Applications." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/203470.

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The term biometrics is used to describe the process of analyzing biological and behavioral traits that are unique to an individual in order to confirm or determine his or her identity. Many biometric modalities are currently being researched and implemented including, fingerprints, hand and facial geometry, iris recognition, vein structure recognition, gait, voice recognition, etc... This project explores the possibility of using corneal topography measurements as a trait for biometric identification. Two new corneal topographers were developed for this study. The first was designed to function as an operator-free device that will allow a user to approach the device and have his or her corneal topography measured. Human subject topography data were collected with this device and compared to measurements made with the commercially available Keratron Piccolo topographer (Optikon, Rome, Italy). A third topographer that departs from the standard Placido disk technology allows for arbitrary pattern illumination through the use of LCD monitors. This topographer was built and tested to be used in future research studies. Topography data was collected from 59 subjects and modeled using Zernike polynomials, which provide for a simple method of compressing topography data and comparing one topographical measurement with a database for biometric identification. The data were analyzed to determine the biometric error rates associated with corneal topography measurements. Reasonably accurate results, between three to eight percent simultaneous false match and false non-match rates, were achieved.
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Imada, Renata Nagima [UNESP]. "Reconhecimento de contorno de edifício em imagens de alta resolução usando os momentos complexos de Zernike." Universidade Estadual Paulista (UNESP), 2014. http://hdl.handle.net/11449/122215.

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Made available in DSpace on 2015-04-09T12:28:28Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-10-24Bitstream added on 2015-04-09T12:47:21Z : No. of bitstreams: 1 000812794.pdf: 1525344 bytes, checksum: b68f6da113153c038916e9bd3f57c375 (MD5)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Nesta pesquisa foi estudado um m etodo de reconhecimento de contornos de telhado de edif cios em imagens digitais de alta resolu c~ao, que classi ca-os com rela c~ao a sua forma. O m etodo baseia-se nos momentos de Zernike, que s~ao baseados nos polin omios ortogonais de Zernike, em que cria-se um vetor de caracter sticas para cada regi~ao da imagem, que deve ser previamente segmentada de maneira que seus objetos sejam divididos em diferentes regi~oes. Este m etodo para a descri c~ao de forma baseia-se na area do objeto de interesse e possui a caracter stica dos momentos serem invariantes em rela c~ao as transforma c~oes geom etricas de rota c~ao, transla c~ao e escala, que o torna atrativo para o problema de an alise de imagem proposto. Desse modo, foi criada uma base de dados contendo esbo cos (ou modelos) de poss veis apari c~oes de contornos de telhado de edif cio numa dada cena, para que seja associado tamb em um vetor de caracter sticas de Zernike para estes esbo cos. Assim, a dist ancia euclidiana entre este vetor e o vetor de caracter sticas calculado a partir de uma regi~ao segmentada na imagem, permite dizer se a regi~ao dada corresponde a um contorno de edif cio ou a outro objeto. A capacidade de discrimina c~ao do m etodo proposto entre diferentes formas de edif cios, e tamb em entre formas de edif cios e n~ao edif cios foi avaliada experimentalmente e mostrou resultados positivos.<br>In this research, a method of recognition of building roof contours in high-resolution digital images which classi es them with respect to their form was studied. The method is based on Zernike moments, which are based on orthogonal Zernike polynomials and it creates a feature vector for each image region. The image segmentation has to be made rst to de ne di erent regions for its objects. This method for shape analysis is based on the object area of interest and the moments has the characteristic of being invariant under geometric transformations of rotation, translation and scaling, this makes it attractive to the proposed image analysis problem. Thus, a database containing sketches (or models) of possible appearances of building roof contours in a given scene was created, so a Zernike feature vector was also associated for these sketches. Therefore, the Euclidean distance between this vector and the feature vector calculated from a segmented region in the image lets say if the given region corresponds to a building contour or other object. The capacity of the proposed method in discriminating di erent building shapes and also in discriminating building shapes from non-building shapes was evaluated experimentally and it showed positive results.
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Imada, Renata Nagima. "Reconhecimento de contorno de edifício em imagens de alta resolução usando os momentos complexos de Zernike /." Presidente Prudente, 2014. http://hdl.handle.net/11449/122215.

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Orientador: Aluir Porfírio Dal Poz<br>Banca: Edson Aparecido Mitishita<br>Banca: Aylton Pagamisse<br>Resumo: Nesta pesquisa foi estudado um m etodo de reconhecimento de contornos de telhado de edif cios em imagens digitais de alta resolu c~ao, que classi ca-os com rela c~ao a sua forma. O m etodo baseia-se nos momentos de Zernike, que s~ao baseados nos polin^omios ortogonais de Zernike, em que cria-se um vetor de caracter sticas para cada regi~ao da imagem, que deve ser previamente segmentada de maneira que seus objetos sejam divididos em diferentes regi~oes. Este m etodo para a descri c~ao de forma baseia-se na area do objeto de interesse e possui a caracter stica dos momentos serem invariantes em rela c~ao as transforma c~oes geom etricas de rota c~ao, transla c~ao e escala, que o torna atrativo para o problema de an alise de imagem proposto. Desse modo, foi criada uma base de dados contendo esbo cos (ou modelos) de poss veis apari c~oes de contornos de telhado de edif cio numa dada cena, para que seja associado tamb em um vetor de caracter sticas de Zernike para estes esbo cos. Assim, a dist^ancia euclidiana entre este vetor e o vetor de caracter sticas calculado a partir de uma regi~ao segmentada na imagem, permite dizer se a regi~ao dada corresponde a um contorno de edif cio ou a outro objeto. A capacidade de discrimina c~ao do m etodo proposto entre diferentes formas de edif cios, e tamb em entre formas de edif cios e n~ao edif cios foi avaliada experimentalmente e mostrou resultados positivos.<br>Abstract: In this research, a method of recognition of building roof contours in high-resolution digital images which classi es them with respect to their form was studied. The method is based on Zernike moments, which are based on orthogonal Zernike polynomials and it creates a feature vector for each image region. The image segmentation has to be made rst to de ne di erent regions for its objects. This method for shape analysis is based on the object area of interest and the moments has the characteristic of being invariant under geometric transformations of rotation, translation and scaling, this makes it attractive to the proposed image analysis problem. Thus, a database containing sketches (or models) of possible appearances of building roof contours in a given scene was created, so a Zernike feature vector was also associated for these sketches. Therefore, the Euclidean distance between this vector and the feature vector calculated from a segmented region in the image lets say if the given region corresponds to a building contour or other object. The capacity of the proposed method in discriminating di erent building shapes and also in discriminating building shapes from non-building shapes was evaluated experimentally and it showed positive results.<br>Mestre
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Wichitwong, Wisuttida. "Application of digital holography for metrology of inclusions in a droplet." Thesis, Rouen, INSA, 2015. http://www.theses.fr/2015ISAM0007/document.

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Dans cette thèse, l'holographie numérique dans l'axe (DIH) est la principale méthode optique utilisée pour analyser des inclusions dans une gouttelette. L'holographie numérique dans l'axe est utilisée pour caractériser des inclusions du point de vue de leur taille, leur position 3D et leur trajectoire à l'intérieur de la gouttelette. Comme les particules sont situées à l'intérieur d'une gouttelette, le front d'onde incident sur l'inclusion est modifié avant qu'il l'illumine. Le défi de ce travail est double : premièrement de prendre en compte la forme de la gouttelette dans le modèle d'holographie et deuxièmement d'étendre l'analyse aux inclusions transparentes (type objet de phase). Pour décrire l'hologramme enregistré par le capteur CCD, l'intégrale d'Huygens-Fresnel et le formalisme des matrices ABCD ont été utilisés. Dans ce modèle, nous introduisons les polynômes de Zernike pour décrire la fonction de transmission d'une particule. Pour l'analyse des hologrammes, l'outil mathématique de la transformation de Fourier fractionnaire 2D (2D-FRFT) est utilisé pour restituer l'image des inclusions et dans ce cas une mesure la taille de l'inclusion et de sa position 3D sont réalisées. Les trajectoires des inclusions dans la goutte est possible avec un long temps de pose de l'obturateur du capteur CCD. Nous avons également proposé un nouveau modèle pour décrire des objets de phases quelconque et des particules opaques. Pour ce nouveau modèle, les mêmes procédés ont été utilisés. Dans le cas d'inclusions filiformes à l'intérieur d'une géométrie cylindrique comme un canal, une méthode de simulation d'imagerie interférométrique multi-coeurs est proposée. Dans ce cas, une somme de distributions de Dirac, localisées le long d'une droite, introduite dans l'intégrale de Fresnel généralisée (c'est-à-dire le formalisme des matrices ABCD et l'intégrale de Fresnel) permet d'obtenir un bon degré de similitude entre l'expérience et la simulation<br>In this thesis, the digital in-line holography (DIH) is the main optical method used to analyze inclusions in a droplet. The digital in-line holography is used to characterize the inclusions in terms of of their size, their 3D position, and their trajectories inside the droplet. Since the particles are located within a droplet, the incident wavefront is changed before it illuminates the inclusions. The challenge of this work has two points : first to take into account the shape of the droplet in the holographic model and secondly to extend the analysis to the transparent inclusions (phase object). To describe the hologram recorded by the CCD sensor, the Huygens-Fresnel integral and the ABCD matrix formalism were used. In this model, we introduce the Zernike polynomials to describe the transmission function of a particle. For the analysis of holograms, the2D fractional Fourier transformation (2D-FRFT) is used to reconstruct the image of inclusions and in this case the size and their 3D position of the inclusions are performed.The trajectories of the inclusions in the drop are possible tracked with a long exposure shutter speed of the CCD. We also proposed a new simulation to describe objects of any phases and opaque particles. For this simulation, the same methods of reconstruction were used. In the case of micro-channel inclusions inside a cylindrical geometry such as a pipe, the interferometric imaging of multi-core pipe is proposed. In this case, summation of Dirac delta distribution, located along a line, introduced into the generalized Fresnel integral allows us to get a good agreement between the experiment and the simulation
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Books on the topic "Zernike"

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Pitstra, Froukje. Ontelbare enkelvouden: Dr. Anne Mankes-Zernike (1887-1972) : een biografie. Uitgeverij Meinema, 2014.

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2

Kubbinga, Henk, ed. The Collected Papers of Frits Zernike (1888-1966): Volumes I, II, III, IV. Groningen University Press, 2012.

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3

Structure and thermodynamics of lattice polymers in bulk and at interfaces: A comparison of Ornstein-Zernike-like approaches to Monte Carlo simulations. University of Eindhoven, 1996.

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4

Hnilami͡odaŭ, Uladzimir Vasilʹevich. Praŭda zerni͡a: Tvorchy partrėt Vasili͡a Zui͡onka. Mastat͡skai͡a Lit-ra, 1992.

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Anton, Hornung Rodríguez, ed. Familienbuch der katholischen Pfarrgemeinde Deutsch Zerne im Banat: Deutsch Cernya, Nemet-Czernya, Nemetczernya, Nemacka-Crnja : 1808-1918/1946 : auf der Grundlage der Kirchenbücher von Deutsch Zerne mit Serbisch Zerne und Tomsdorf-Hettin. Arbeitsgemeinschaft für Veröffentlichung Banater Familienbücher, 2009.

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Nieske, Christian. Vom Land und seinen Leuten: Leben in einem Mecklenburger Bauerndorf 1750 bis 1953. T. Helms, 1997.

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Frits Zernike: Groninger nobelprijsdrager, 1888-1966. North-Holland, 1988.

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H, Brinkman, and Zernike Frits 1888-1966, eds. Frits Zernike: Groninger nobelprijsdrager, 1888-1966. Universiteitsmuseum Groningen, 1988.

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Sovet, Russia (Federation) Verkhovnyĭ, ed. Zakon Rossiiskoĭ Federatsii o zerne: Postanovelnii︠a︡ VS. Dioniks, 1993.

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Book chapters on the topic "Zernike"

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Shekhar, Shashi, and Hui Xiong. "Zernike." In Encyclopedia of GIS. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-35973-1_1510.

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Shekhar, Shashi, and Hui Xiong. "Zernike Polynomials." In Encyclopedia of GIS. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-35973-1_1511.

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Bühren, Jens. "Zernike Coefficients." In Encyclopedia of Ophthalmology. Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-642-35951-4_450-4.

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Sokollik, Thomas. "Zernike Polynomials." In Investigations of Field Dynamics in Laser Plasmas with Proton Imaging. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-15040-1_14.

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Bühren, Jens. "Zernike Coefficients." In Encyclopedia of Ophthalmology. Springer Berlin Heidelberg, 2018. http://dx.doi.org/10.1007/978-3-540-69000-9_450.

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Atakishiyev, Natig M., George S. Pogosyan, Cristina Salto-Alegre, Kurt Bernardo Wolf, and Alexander Yakhno. "The Superintegrable Zernike System." In Springer Proceedings in Mathematics & Statistics. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2715-5_16.

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Bastos, Igor L. O., Larissa Rocha Soares, and William Robson Schwartz. "Pyramidal Zernike Over Time: A Spatiotemporal Feature Descriptor Based on Zernike Moments." In Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75193-1_10.

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Bakar, Norsharina Abu, and Siti Mariyam Shamsuddin. "United Zernike Invariants for Character Images." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05036-7_47.

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Xin, Yongqing, Miroslaw Pawlak, and Simon Liao. "Image Reconstruction with Polar Zernike Moments." In Pattern Recognition and Image Analysis. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11552499_45.

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Liao, Simon X., and Miroslaw Pawlak. "A study of Zernike moment computing." In Computer Vision — ACCV'98. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-63930-6_146.

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Conference papers on the topic "Zernike"

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Bubis, E. L., and A. Z. Matveev. "Photothermal Zernike filter." In The International Conference on Coherent and Nonlinear Optics, edited by Vladimir N. Belyi, Konstantin N. Drabovich, and Christos Flytzanis. SPIE, 2007. http://dx.doi.org/10.1117/12.751874.

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Bernardes, José, Pedro Sampaio, Kamila Gomes, Iális De Paula Júnior, and Marcelo De Souza. "Classificação de Objetos usando os momentos de Zernike." In Escola Regional de Computação Ceará, Maranhão, Piauí. Sociedade Brasileira de Computação - SBC, 2020. http://dx.doi.org/10.5753/ercemapi.2020.11480.

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Abstract:
Os momentos de Zernike são conjuntos de polinômios complexos usados em problemas de visão computacional e existem diversos trabalhos que exploram as suas propriedades descritor de atributos que se apresenta invariável a rotação. Neste artigo, é explorado o desempenho dos momentos de Zernike em um problema de classificação ao qual os conjuntos de cada classe possuem uma variedade de perspectivas. Para isso, foi utilizado a base de dados Natural Images e três algoritmos de aprendizado de máquina.Com o intuito de trazer uma comparação e mostrar os impactos das variações dos parâmetros nos desempenho dos algoritmos. Ao final do trabalho, o melhor resultado obtido foi o de 77% de acurácia.
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Mahajan, Virendra N. "Zernike Polynomials and Beyond." In Latin America Optics and Photonics Conference. OSA, 2010. http://dx.doi.org/10.1364/laop.2010.tuh2.

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Williamson, David M. "Frits Zernike and microlithography." In SPIE Optical Systems Design, edited by Laurent Mazuray, Rolf Wartmann, and Andrew P. Wood. SPIE, 2015. http://dx.doi.org/10.1117/12.2191129.

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Genberg, Victor L., Gregory J. Michels, and Keith B. Doyle. "Orthogonality of Zernike polynomials." In International Symposium on Optical Science and Technology, edited by Alson E. Hatheway. SPIE, 2002. http://dx.doi.org/10.1117/12.482169.

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Yun Guo, Chunping Liu, and Shengrong Gong. "Improved algorithm for Zernike moments." In 2015 International Conference on Control, Automation and Information Sciences (ICCAIS). IEEE, 2015. http://dx.doi.org/10.1109/iccais.2015.7338682.

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Grey, Louis D. "Regression Analysis Of Zernike Polynomials." In 31st Annual Technical Symposium. SPIE, 1987. http://dx.doi.org/10.1117/12.978912.

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Mahajan, Virendra N. "Zernike polynomials and aberration balancing." In Optical Science and Technology, SPIE's 48th Annual Meeting, edited by Pantazis Z. Mouroulis, Warren J. Smith, and R. Barry Johnson. SPIE, 2003. http://dx.doi.org/10.1117/12.511384.

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Sheppard, Colin J. R. "Three topics in Zernike polynomials." In Photonics Europe, edited by Frank Wyrowski. SPIE, 2004. http://dx.doi.org/10.1117/12.564935.

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Singh, Chandan, Ekta Walia, and Neerja Mittal. "Magnitude and Phase Coefficients of Zernike and Pseudo Zernike Moments for Robust Face Recognition." In Robotics and Applications. ACTAPRESS, 2011. http://dx.doi.org/10.2316/p.2011.740-016.

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Reports on the topic "Zernike"

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Vine, David, Wenbing Yun, Sylvia Lewis, Alan Lyon, Richard Ian Spink, and Benjamin Stripe. Development of a laboratory Transmission X-ray Microscope using Zernike Phase Contrast at 2.7 keV X-rays for Imaging Biological Specimens with 30nm Resolution in 3D. Office of Scientific and Technical Information (OSTI), 2019. http://dx.doi.org/10.2172/1492705.

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